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Cubature Method for Stochastic Volterra Integral Equations [article]

Qi Feng, Jianfeng Zhang
2022 arXiv   pre-print
In this paper, we introduce the cubature formulas for Stochastic Volterra Integral Equations. We first derive the stochastic Taylor expansion in this setting and provide its tail estimates.  ...  We then introduce the cubature measure for such equations, and construct it explicitly in some special cases, including a long memory stochastic volatility model.  ...  To introduce the cubature method for SVIEs, our first step is to derive the stochastic Taylor expansion in this setting.  ... 
arXiv:2110.12853v2 fatcat:cm2k5m3o4beshpisrec64nnz74

Page 616 of Mathematical Reviews Vol. , Issue 83b [page]

1983 Mathematical Reviews  
Authors’ summary: “The need for providing reliable numerical methods for the solution of weakly singular Volterra integral equations of the first kind stems from the fact that they are connected to important  ...  s3b:45 002 45A Linear integral equations See also 46056. Moraru, N. I. 83b:45002 A two-dimensional convolution-type integral equation solvable in cubatures.  ... 

Page 6029 of Mathematical Reviews Vol. , Issue 2001I [page]

2001 Mathematical Reviews  
Graham, Nu- merical methods for integral equations of Mellin type (423-437); A. Rathsfeld, Quadrature methods for 2D and 3D problems (439- 460); Ian H. Sloan, Qualocation (461—478); W.  ...  Wendland, Domain decomposition methods via boundary integral equations (521-537).  ... 

Page 338 of Mathematical Reviews Vol. , Issue 84a [page]

1984 Mathematical Reviews  
Daniel; Sankar, R. 84a:65107 The method of successive updated iterated defect correction and its application to second kind Volterra integral equations. BIT 22 (1982), no. 3, 390-394.  ...  The authors describe a method of successive updated iterated defect correction as applied to the Volterra equation v(x)=f(x)+ [°K (x.t,9(0)de, O0<x<a.  ... 

Deterministic Variational Inference for Neural SDEs [article]

Andreas Look, Melih Kandemir, Jan Peters
2021 arXiv   pre-print
Neural Stochastic Differential Equations (NSDEs) model the drift and diffusion functions of a stochastic process as neural networks.  ...  Existing SDE inference methods either make overly restrictive assumptions, e.g. linearity, or rely on Monte Carlo integration that requires many samples at prediction time for reliable uncertainty quantification  ...  I Stochastic Lotka-Volterra Equation We choose the true dynamics of stochastic Lotka-Volterra equations as in [Abbati et al., h(t + k−1 ) h(t − k ) h(t + k ) h(t − k ) (b) Architecture used for USHCN  ... 
arXiv:2006.08973v4 fatcat:bzx5njyzzbb4lfw7zri33ca3ni

Page 3141 of Mathematical Reviews Vol. 58, Issue 5 [page]

1979 Mathematical Reviews  
Kuznetihina, Application of nonclosed cubature formulas for the numerical solution of two-di- mensional nonlinear integral equations of Volterra type (pp. 136- 151); T. I. Nazarenko and L. V.  ...  Maréenko, An interval method for the solution of integro-differential equations of Volterra type (pp. 152-160); M. A. Dmitrieva, Estimation of the convergence of  ... 

Author Index Volume 231 (2009)

2009 Journal of Computational and Applied Mathematics  
Jiang, On a graded mesh method for a class of weakly singular Volterra integral equations 807-814 Ma, L. and Z.  ...  some weakly singular linear Volterra integral equations 725-734 Basto, M., V.  ... 
doi:10.1016/s0377-0427(09)00371-9 fatcat:v6qmsedjjbcrjm477ln6hapnhi

Page 1793 of Mathematical Reviews Vol. 56, Issue 5 [page]

1978 Mathematical Reviews  
There is a wealth of examples of applications: the equation of a vibrating beam, Fredholm equations of the second kind, a non-linear Volterra equation, Fresnel integrals.  ...  Authors’ summary: “Factorial series are used for deriving a method of successive solutions of parameter-plane equations for real, uniform, and positive increments in the complex variable.  ... 

Dynamic modeling of neuronal responses in fMRI using cubature Kalman filtering

Martin Havlicek, Karl J. Friston, Jiri Jan, Milan Brazdil, Vince D. Calhoun
2011 NeuroImage  
using a highly efficient numerical integration method 295 (cubature rules).  ...  differential equations (SDE) in (1) can 197 also be expressed using Riemann and Ito integrals (Kloeden and Platen, second integral is stochastic.  ...  To pursue this issue of identifiably we examined the three remaining parameters to the previous models, the SCKF alone was not sufficient for successful estimation of the states 999 and input.  ... 
doi:10.1016/j.neuroimage.2011.03.005 pmid:21396454 pmcid:PMC3105161 fatcat:inmlnzsgsbg37mzop3jzf7ikqi

Neural Differential Equations as a Basis for Scientific Machine Learning (SciML) [article]

Christopher Rackauckas
2020 figshare.com  
Additionally, deep learning embedded within backwards stochastic differential equations has been shown to be an effective tool for solving high-dimensional partial differential equations, like the Hamilton-Jacobian-Bellman  ...  In this talk we will introduce the audience to these methods and show how these diverse methods are all instantiations of a neural differential equation, a differential equation where all or part of the  ...  Adaptive high order methods for stochastic differential equations  Stiff state-dependent delay differential equation discontinuity tracking  Mix in Gillespie simulation (Continuous-Time Markov Chains  ... 
doi:10.6084/m9.figshare.12751955.v1 fatcat:zhwjvt23tfhmjljetsfobsv5q4

subject index volumes 201 to 210

2007 Journal of Computational and Applied Mathematics  
Vertex 205 497 Viscosity solution 204 537 Volterra 205 736, 744 Volterra delay-integro-differential equation 206 898 Volterra difference equations 205 859 Volterra integral equation 206 801 Volterra integral  ...  systems 202 3 Integral averaging techniques 202 460 Integral boundary equations 206 473 Integral equations 204 440; 205 479, 849 Integral inequality 205 479 Integral iterative method 209 167 Integral  ... 
doi:10.1016/s0377-0427(07)00502-x fatcat:tovvilkoczetvl423gcjxug7gm

Index

2000 Journal of Computational and Applied Mathematics  
Nelson, Variable transformations in the numerical solution of second kind Volterra integral equations with continuous and weakly singular kernels; extensions to Fredholm integral equations 115 (2000) 193  ...  MuK ller, A collocation method for nonlinear Cauchy singular integral equations 115 (2000) 283}300 Kalantari, B. and J.  ... 
doi:10.1016/s0377-0427(00)00525-2 fatcat:rdbpwy2pxndlrbesc4azeci34y

Author Index Volume 224 (2009)

2009 Journal of Computational and Applied Mathematics  
Mohammad Hosseini, On mean-square stability properties of a new adaptive stochastic Runge-Kutta method 556-564 Fu, X. and X.  ...  Song, Kernel method and system of functional equations 133-139 Marcozzi, M.D., Extrapolation discontinuous Galerkin method for ultraparabolic equations 679-687 Martínez, E., see Hueso, J.L. 77-83 McBain  ... 
doi:10.1016/s0377-0427(08)00661-4 fatcat:klihhk5hxngjdgg6fy56yenaxi

Author Index Volume 235 (2011)

2011 Journal of Computational and Applied Mathematics  
Shardlow, The exponential integrator scheme for stochastic partial differential equations: Pathwise error bounds 1245-1260 Klus, S., T. Sahai, C. Liu and M.  ...  Burrage, Supplement: Efficient weak second order stochastic Runge-Kutta methods for non-commutative Stratonovich stochastic differential equations 5326-5329 Kong, L., J. Hong, F. Fu and J.  ... 
doi:10.1016/s0377-0427(11)00383-9 fatcat:iydszqpkezgivirtbnwhpwere4

Indices

1977 Mathematics of Computation  
J. 265 On a Boundary Extrapolation Theorem by Kreiss . 469 Taylor Series Methods for the Solution of Volterra Integral and Integro-Differential Equations . 691 On the Stability of Galerkin Methods for  ...  6.15 Integral Equations ATKINSON, KENDALL E. 2 A Survey of Numerical Methods for the Solution of Fredholm Integral Equations of the Second Kind 322 7.00 Special Functions HANSEN, ELDON R. 10 A Table of  ... 
doi:10.1090/s0025-5718-77-99986-0 fatcat:c6c5g4gy2ngf5ln3b5thbtxhx4
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